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Co-prime arrays can estimate the directions of arrival (DOAs) of scriptO(MN) sources with scriptO(M+N) sensors, and are convenient to analyze due to their closed-form expression for the locations of virtual lags. However, the number of degrees of freedom is limited due to the existence of holes in difference coarrays if subspace-based algorithms such as the spatial smoothing multiple signal classification (MUSIC) algorithm are utilized. To address this issue, techniques such as positive definite Toeplitz completion and array interpolation have been proposed in the literature. Another factor that compromises the accuracy of DOA estimation is the limitation of the number of snapshots. Coarray-based processing is particularly sensitive to the discrepancy between the sample covariance matrix and the ideal covariance matrix due to the finite number of snapshots. In this paper, coarray interpolation based on matrix completion (MC) followed by a denoising operation is proposed to detect more sources with a higher accuracy. The effectiveness of the proposed method is based on the capability of MC to fill in holes in the virtual sensors and that of MC denoising operation to reduce the perturbation in the sample covariance matrix. The results of numerical simulations verify the superiority of the proposed approach.

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Aiming at the recognition of low-probability-of-intercept (LPI) radar signals, a support vector machine (SVM)-based algorithm is proposed, where the information geometry theory is utilised to optimise the kernel function of the SVM. Since signals with different modulations have different characteristics in the time-frequency domain, the timefrequency transformation result of the LPI radar signal is considered as an image, referred to as the time-frequency image, and computer vision techniques are utilized to perform recognition. Specifically, the time-frequency images of different LPI radar signals are obtained via the Choi-Williams distribution (CWD) transform, and the AlexNet network, one improved convolutional neural network (CNN), is used to extract time-frequency features. Then, an SVM is adopted to recognise LPI radar signals due to its superiority in addressing the dimension disaster and non-linear inseparability issue. The extracted time-frequency features are fed into the SVM for classification and recognition. Note that the classification performance of SVM depends on the kernel function. Therefore, in the proposed algorithm, information geometry theory is exploited to improve the Gaussian kernel function, and the maximum margin between different categories of samples is further enlarged. As a consequence, the recognition accuracy for LPI radar signals with similar time-frequency images is effectively improved. In addition, the proposed algorithm has better robustness to small samples than other deep learning-based algorithms, since the SVM method minimises the structural risk instead of the empirical risk. Simulation results verify the effectiveness of the proposed algorithm.